A Computational Evaluation of the Steric and Electronic Contributions in Stereoselective Olefin Polymerization with Pyridylamido-Type Catalysts

A density functional theory (DFT) study combined with the steric maps of buried volume (%VBur) as molecular descriptors and an energy decomposition analysis through the ASM (activation strain model)–NEDA (natural energy decomposition analysis) approach were applied to investigate the origins of stereoselectivity for propene polymerization promoted by pyridylamido-type nonmetallocene systems. The relationships between the fine tuning of the ligand and the propene stereoregularity were rationalized (e.g., the metallacycle size, chemical nature of the bridge, and substituents at the ortho-position on the aniline moieties). The DFT calculations and %VBur steric maps reproduced the experimental trend: substituents on the bridge and on the ortho-positions of aniline fragments enhance the stereoselectivity. The ASM–NEDA analysis enabled the separation of the steric and electronic effects and revealed how subtle ligand modification may affect the stereoselectivity of the process.


Introduction
The advent of single-site α-olefin polymerization catalysts has revolutionized the world of polyolefins, as they enable the fine tuning of polymer microstructures in terms of stereoregularity [1], regioregularity [2,3] molecular mass [4][5][6], and polymer properties [7]. Increasing interest in the design of novel nonmetallocene complexes [8] has also opened up a way to further investigate the factors that determine the origin of the stereocontrol of α-olefin polymerization promoted by homogeneous systems. Some interesting examples of this are the pyridylamido-Hf catalyst model compounds developed by Coates et al. [9] (Ia, Ib, Chart 1) and the modification [10] (IIa-IId, Chart 1) of Dow Chemical systems [11] obtained via high-throughput technologies (IIe, Chart 1). Besides propylene, systems IIc and IIe (Chart 1) have been also employed to polymerize higher α-olefins such as 1-hexene and 1-octene [12], as well as to incorporate functional comonomers [13]. Moreover, block copolymers can be obtained through "chain shuttling" processes, which involve IIe in combination with a second catalyst [14][15][16][17]. Density functional theory (DFT) calculations have revealed that IIa-IIe produce isotactic polypropylenes (iPP), despite the C 1 or C s symmetry of the catalyst precursors, through a combination of peculiar aspects that distinguish this class of complexes, which are briefly summarized here. The cationic species deriving from the cocatalyst activation show both the Hf-C Aryl and Hf-C Alkyl bonds into which the first olefin insertion may occur, and it has been demonstrated that the initial insertion takes place at the Hf-C Aryl bond, thus generating the monoinserted active species (Scheme 1) [18][19][20][21].
The DFT calculations also found a substantial preference for propene insertion at one of the two diastereotopic sites thus generated (Scheme 1) [22], leading to a chain stationary (CS) mechanism (or site epimerization) [23] different from the usual chain migratory (CM) mechanism (the switching of the olefin and the growing chain at each insertion step) [24]. Very recently [25,26], we identified the stereo-electronic factors that induce a CS mechanism by using a combined approach based on DFT calculations, a sterical descriptor (the percentage of occupied volume (%VBur) [27,28]), and an activation strain model (ASM) with a natural energy decomposition analysis (NEDA) scheme [29,30], which were applied to polymerization catalysis [31,32].
This family of catalysts deviates from the classical "chiral growing chain orientation" mechanism of stereocontrol [1,33] operating on ansa-metallocene [1] and heterogeneous Ziegler-Natta (ZN) systems [33,34], because its stereoselectivity is indeed based on a direct monomer-ligand interaction mechanism [22]. The experimental propene polymerization data (Table S1) show that the ortho-substituents on the aniline moiety (R in Chart 1) play a crucial role in the stereoselectivity, with the catalyst performance also being influenced by the R 1 and R 2 substituents on the bridge linking the pyridine and the N-aryl fragment (Chart 1). Although quite far from the active sites, they do affect the enantioselectivity of the complex, pushing the N-aryl ring, and consequently its ortho-substituent, closer to the active site thus, enhancing the stereoselectivity of the catalyst through a "buttressing effect" [10]. Furthermore, Hagadorn et al. [35] claimed that a substitution of the C-bridge with a Si-bridge (IIIa, IIIb, Chart 1) seems to increase the stereoselectivity of propene polymerization. Finally, a replacement of the aryl group (e.g., phenyl or naphthyl) with heteroaryls [36,37] has also been reported. For instance, Pellecchia et al. synthesized a Cs-Chart 1. Systems analyzed in this study.
Molecules 2023, 28, x FOR PEER REVIEW 2 of 13 Chart 1. Systems analyzed in this study.
The DFT calculations also found a substantial preference for propene insertion at one of the two diastereotopic sites thus generated (Scheme 1) [22], leading to a chain stationary (CS) mechanism (or site epimerization) [23] different from the usual chain migratory (CM) mechanism (the switching of the olefin and the growing chain at each insertion step) [24]. Very recently [25,26], we identified the stereo-electronic factors that induce a CS mechanism by using a combined approach based on DFT calculations, a sterical descriptor (the percentage of occupied volume (%VBur) [27,28]), and an activation strain model (ASM) with a natural energy decomposition analysis (NEDA) scheme [29,30], which were applied to polymerization catalysis [31,32].
This family of catalysts deviates from the classical "chiral growing chain orientation" mechanism of stereocontrol [1,33] operating on ansa-metallocene [1] and heterogeneous Ziegler-Natta (ZN) systems [33,34], because its stereoselectivity is indeed based on a direct monomer-ligand interaction mechanism [22]. The experimental propene polymerization data (Table S1) show that the ortho-substituents on the aniline moiety (R in Chart 1) play a crucial role in the stereoselectivity, with the catalyst performance also being influenced by the R 1 and R 2 substituents on the bridge linking the pyridine and the N-aryl fragment (Chart 1). Although quite far from the active sites, they do affect the enantioselectivity of the complex, pushing the N-aryl ring, and consequently its ortho-substituent, closer to the active site thus, enhancing the stereoselectivity of the catalyst through a "buttressing effect" [10]. Furthermore, Hagadorn et al. [35] claimed that a substitution of the C-bridge with a Si-bridge (IIIa, IIIb, Chart 1) seems to increase the stereoselectivity of propene polymerization. Finally, a replacement of the aryl group (e.g., phenyl or naphthyl) with heteroaryls [36,37] has also been reported. For instance, Pellecchia et al. synthesized a Cs-Scheme 1. Ligand modification with the monomer via α-olefin insertion into Hf-aryl bond [18][19][20][21].
The DFT calculations also found a substantial preference for propene insertion at one of the two diastereotopic sites thus generated (Scheme 1) [22], leading to a chain stationary (CS) mechanism (or site epimerization) [23] different from the usual chain migratory (CM) mechanism (the switching of the olefin and the growing chain at each insertion step) [24]. Very recently [25,26], we identified the stereo-electronic factors that induce a CS mechanism by using a combined approach based on DFT calculations, a sterical descriptor (the percentage of occupied volume (%V Bur ) [27,28]), and an activation strain model (ASM) with a natural energy decomposition analysis (NEDA) scheme [29,30], which were applied to polymerization catalysis [31,32].
This family of catalysts deviates from the classical "chiral growing chain orientation" mechanism of stereocontrol [1,33] operating on ansa-metallocene [1] and heterogeneous Ziegler-Natta (ZN) systems [33,34], because its stereoselectivity is indeed based on a direct monomer-ligand interaction mechanism [22]. The experimental propene polymerization data (Table S1) show that the ortho-substituents on the aniline moiety (R in Chart 1) play a crucial role in the stereoselectivity, with the catalyst performance also being influenced by the R 1 and R 2 substituents on the bridge linking the pyridine and the N-aryl fragment (Chart 1). Although quite far from the active sites, they do affect the enantioselectivity of the complex, pushing the N-aryl ring, and consequently its ortho-substituent, closer to the active site thus, enhancing the stereoselectivity of the catalyst through a "buttressing effect" [10]. Furthermore, Hagadorn et al. [35] claimed that a substitution of the C-bridge with a Si-bridge (IIIa, IIIb, Chart 1) seems to increase the stereoselectivity of propene polymerization. Finally, a replacement of the aryl group (e.g., phenyl or naphthyl) with heteroaryls [36,37] has also been reported. For instance, Pellecchia et al. synthesized a C s -symmetric Zr(IV) complex which bears a tridentate pyrrolidepyridine ligand (IVa, Chart 1) and affords iPP when combined with Al i Bu 2 H and methylalumoxane [38]. The presence of Al-H alkyl species is necessary for making the complex stereoselective, and the DFT calculations suggest [39] that Al coordinates with the N pyrrolic and that H interacts with the central metal, leading to a sort of "ligand modification", similar to what happens for pyridylamido Hf catalysts. The original catalyst symmetry is thus altered by the Al i Bu 2 H coordination, shifting from C s to C 1 symmetry. The two diastereotopic active sites, one which is better described by a pyramidal square geometry (site 1) and the other by a trigonal bypiramidal geometry (site 2), select the same propene enantioface, with the unprecedented combination of a "direct ligand-monomer" interaction for one site and a "chiral growing chain orientation" model for the other [39].
In this work, we decided to investigate the propene stereoselectivity promoted by the systems of Chart 1 to achieve a unified picture, with respect to the (large) spread of the experimental data (Table S1). We used a combined approach based on DFT calculations, a %V Bur analysis, and an ASM-NEDA model to assess the steric and electronic contributions to the propene stereoselectivity for the fine tuning of: (a) the metallacycle size, characterized by a six-membered (Ia-Ib) and seven-membered (IIa-IIe, IIIa, IIIb) ring, respectively; (b) the chemical nature of the R, R 1 , and R 2 substituents located on the aniline ring and the bridge linking the pyridine and the aniline fragments; (c) the central atom on the bridge by replacing the C with Si atoms (IIIa, IIIb); and (d) the pyridylamido framework by replacing the aryl with heteroaryl groups (IVa).

Results and Discussion
The DFT values calculated for the stereoselectivity of the propene polymerization promoted by the systems of Chart 1 are summarized in Table 1. They are reported as the differences in the electronic energies (free energies) between the lower 1,2 si and 1,2 re propene enantioface insertion transition states (TSs), which were calculated in the presence of a solvent contribution (first column, PCM model, see Section 3). Since the ASM-NEDA analysis employs electronic energies in the gas phase (∆E), for the sake of consistency, we also report the differences in the DFT electronic energies (free energies) values in the gas phase (Table 1, second column). Given the findings about the CS mechanism disclosed for the pyridylamido-Hf complexes [22], only the results for the propene insertion at the preferred site are reported for Ia-IIIb, whereas the energetics for the monomer insertion at both diastereotopic sites are reported for IVa. The partitioning of ∆E Tot into its contributions obtained through the ASM-NEDA analysis is reported in Table 2 and the details about the decomposition of the ∆E Int into all its terms can be found in Table S2. To simplify the discussion, we also added into Table 2 the ∆∆E between the 1,2 re and 1,2 si enantiofaces (kcal/mol) obtained by the ASM-NEDA analysis. The effect of the dispersion corrections on the DFT electronic energies is reported in Table S3, whereas the values of the energetic terms obtained through the ASM-NEDA scheme, without including the dispersion corrections, are illustrated in Table S4.
Looking at the ASM-NEDA results in Table 2, we noted that the ∆E Strain is, indeed, the main factor for the origin of the stereoselectivity promoted by the analyzed systems. The clear preference for the 1,2 re enantioface is only partially compensated by the ∆E Int contribution, which instead stabilizes the si enantioface (Ia-Ib being the only exceptions). The further decomposition of the ∆E Strain into the two components (∆E Strain(Mon) and ∆E Strain(Cat) ) is highly indicative; systems II and III, characterized by the formation of sevenmembered metallacycles, show the propene deformation between the si and re insertions (∆∆E Strain(Mon) ), which outweighs that of the catalyst (∆∆E Strain(Cat) ), thus playing the primary role in the ∆E Strain variation, although the two components become similar for IIe and IIIa (Table 2). Table 1. DFT electronic energies (Gibbs energies) in kcal/mol for the propene stereoselectivity at the preferred site (Ia-IIIb) and at both the diastereotopic active sites (IVa). On the contrary, systems I and IV, which cannot undergo a ligand modification in situ, deviate from this trend, and the ∆∆E Strain(Cat) is the dominant term for the ∆E Strain variation ( Table 2). This difference may be rationalized by examining the orientation of the growing polymer chain obtained by the DFT calculations, taking system Ia as an example. In Figure 1, the optimized geometries for the TSs of the right ( Figure 1A) and wrong propene enantioface insertions ( Figure 1B) promoted by Ia are reported. For such a system, characterized by a six-member metallacycle, there is not enough room to accommodate the bent growing chain [40]; therefore, the catalyst structure distorts and ∆∆E Strain(Cat.) becomes the fundamental contribution to the ∆∆E Strain . For the other pyridylamido catalysts (see, e.g., IIa TS structures reported in Figure 2), the first C-C bond of the i Bu group simulating the polymeryl chain is perfectly in anti with respect to the methyl group of propene, and is thus bent towards the aryl group. It appears that the metallacycle size does affect the iPP stereoselectivity and the results reported in Tables 1 and 2 show that IIa (∆E(∆G) Stereo = 4.0 (3.1) kcal/mol) is more stereoselective than Ia (∆E(∆G) Stereo = 2.4 (1.0) kcal/mol), even if they bear the same R, R 1 , and R 2 substituents, in agreement with the experimental data [9,10] (Table S1). As already mentioned, the ASM-NEDA analysis suggests that the ∆∆E Stereo for Ia is mainly due to the ∆∆E Strain(Cat) contribution, rather than that of the ∆∆E Strain(Mon) ( Table 2) . As a matter of fact, the ∆E Strain(Mon) term favors the wrong propene enantioface insertion (1,2 si) rather than the right one (1,2 re) and the greater distortion of the latter may be attributable to the presence of an additional disfavoring interaction between the propene and naphthyl moiety ( Figure 1A).

∆E(∆G)
Removing this "penalty" with a larger metallacycle (a seven-member metallacycle shown by IIa, Figure 2) forces the naphthyl group to stay further from the olefin and the ∆E Strain(Mon) becomes the main factor in the stereoselectivity ( Table 2).
The variation in the steric hindrance moving from Ia to the IIa active sites may be visualized by the steric maps of the corresponding neutral mono-inserted species ( Figure 3A,B). The northeast (NE) quadrant is effective for the direct monomer enantioface selection, since it contains the N-aryl ring with its ortho-substituents that interact with the "wrong" propene enantioface (1,2 si). At the same time, the southeast (SE) quadrant may be responsible for adding the penalty for the "right" propene enantioface (1,2 re), whereas the southwest (SW) quadrant contains the metallacycles and the naphtyl group. the experimental data [9,10] (Table S1). As already mentioned, the ASM-NEDA analysis suggests that the ΔΔEStereo for Ia is mainly due to the ΔΔEStrain(Cat) contribution, rather than that of the ΔΔEStrain(Mon) ( Table 2). As a matter of fact, the ΔEStrain(Mon) term favors the wrong propene enantioface insertion (1,2 si) rather than the right one (1,2 re) and the greater distortion of the latter may be attributable to the presence of an additional disfavoring interaction between the propene and naphthyl moiety ( Figure 1A). Removing this "penalty" with a larger metallacycle (a seven-member metallacycle shown by IIa, Figure 2) forces the naphthyl group to stay further from the olefin and the ΔEStrain(Mon) becomes the main factor in the stereoselectivity ( Table 2). The variation in the steric hindrance moving from Ia to the IIa active sites may be visualized by the steric maps of the corresponding neutral mono-inserted species ( Figure  3,A,B). The northeast (NE) quadrant is effective for the direct monomer enantioface selection, since it contains the N-aryl ring with its ortho-substituents that interact with the "wrong" propene enantioface (1,2 si). At the same time, the southeast (SE) quadrant may be responsible for adding the penalty for the "right" propene enantioface (1,2 re), whereas the southwest (SW) quadrant contains the metallacycles and the naphtyl group. propene enantioface insertion (1,2 si) rather than the right one (1,2 re) and the greater distortion of the latter may be attributable to the presence of an additional disfavoring interaction between the propene and naphthyl moiety ( Figure 1A). Removing this "penalty" with a larger metallacycle (a seven-member metallacycle shown by IIa, Figure 2) forces the naphthyl group to stay further from the olefin and the ΔEStrain(Mon) becomes the main factor in the stereoselectivity ( Table 2). The variation in the steric hindrance moving from Ia to the IIa active sites may be visualized by the steric maps of the corresponding neutral mono-inserted species ( Figure  3,A,B). The northeast (NE) quadrant is effective for the direct monomer enantioface selection, since it contains the N-aryl ring with its ortho-substituents that interact with the "wrong" propene enantioface (1,2 si). At the same time, the southeast (SE) quadrant may be responsible for adding the penalty for the "right" propene enantioface (1,2 re), whereas the southwest (SW) quadrant contains the metallacycles and the naphtyl group. The computed %V Bur are consistent with the ASM-NEDA results. In fact, the ∆∆E Strain(Mon) term is the main ∆∆E Strain contribution to the system showing the higher %V Bur in the NE quadrant (IIa). Furthermore, although the SW quadrants of the maps for Ia and IIa have comparable buried volumes (81.2% for Ia and 82% for IIa), the SE quadrant for Ia has a significantly higher %V Bur (38.7%) than IIa (33.1%). The greater steric hindrance in the SE quadrant for system Ia is due to the closer proximity of the naphtyl ring to the active site, caused by the smaller metallacycle size. Consequently, the aryl fragment occupies the SE quadrant along with the SW quadrant, thus adding a small penalty to the "right" propene enantioface insertion in the case of catalyst Ia ( Figure 3A). Instead, such a penalty is absent for complex IIa, where the naphtyl moiety occupies only the SW quadrant ( Figure 3B); therefore, it does not interact sterically with the re propene enantioface.
The %V Bur steric maps separated by quadrants allow us also to visualize the effect of the substituents R 1 and R 2 on the CCN bridge by comparing IIa and IIc ( Figure 3B,C). Through the DFT calculations, we found that the ∆E(∆G) Stereo for system IIa is higher than that for IIc (Table 1), and the ASM-NEDA analysis reveals that the main reason for this energetic difference is the ∆∆E Strain , whereas the ∆∆E Int is quite similar ( Table 2). In particular, the ∆∆E Strain(Mon) contribution is larger than the ∆∆E Strain(Cat) term and it increases from IIc to IIa. Indeed, as already reported by Coates et al., bulky substituents at the C-bridge enhance the stereoselectivity through a Thorpe-Ingold-like "buttressing effect", as they interact with ortho-substituents on the aniline ring, forcing them closer to the olefin [10]. This explains the greater distortion of the monomer for IIa rather than IIc, but also the longer distance between the propene and i Pr group on the aniline moiety in the 1,2 si insertion TS for IIc ( Figure S1) with respect to IIa (Figure 2). The influence of the "buttressing effect" becomes evident when the north quadrants of the steric maps are examined. In fact, the presence of different substituents at the bridge not only affects the %V Bur of the northwest (NW) quadrant, but also the buried volume in the NE quadrant, which contains the aniline moiety. Both the NW and NE quadrants of the IIc map ( Figure 3C) have a lower buried volume (73.8% and 45.3%) than the analogous of IIa (75.7% and 50.5%) ( Figure 3B). Furthermore, the substitution of the R substituents with smaller groups (from i Pr to Me) clearly decreases the stereoselectivity of the propene insertion for both the Ib and IIb catalysts ( Table 1). The corresponding DFT-optimized geometries showing less effective ligand-monomer interactions are reported in Figures S2 and S3 and the %V Bur steric maps are reported in Figure S4A,B.  Propene drawing is reported in yellow. The steric hindrance of the ligand framework is described through a color scale (on the right), which ranges from red to blue colors, indicating the more-and less-hindered zones, respectively.
The computed %VBur are consistent with the ASM-NEDA results. In fact, the ΔΔE-Strain(Mon) term is the main ΔΔEStrain contribution to the system showing the higher %VBur in the NE quadrant (IIa). Furthermore, although the SW quadrants of the maps for Ia and IIa have comparable buried volumes (81.2% for Ia and 82% for IIa), the SE quadrant for Ia has a significantly higher %VBur (38.7%) than IIa (33.1%). The greater steric hindrance in the SE quadrant for system Ia is due to the closer proximity of the naphtyl ring to the active site, caused by the smaller metallacycle size. Consequently, the aryl fragment occupies the SE quadrant along with the SW quadrant, thus adding a small penalty to the "right" propene enantioface insertion in the case of catalyst Ia ( Figure 3A). Instead, such a penalty is absent for complex IIa, where the naphtyl moiety occupies only the SW quadrant ( Figure 3B); therefore, it does not interact sterically with the re propene enantioface. The %VBur steric maps separated by quadrants allow us also to visualize the effect of the substituents R 1 and R 2 on the CCN bridge by comparing IIa and IIc (Figure 3B,C). The steric hindrance of the ligand framework is described through a color scale (on the right), which ranges from red to blue colors, indicating the more-and less-hindered zones, respectively.
An interesting modification of the chemical nature of the bridge (replacing the central C atom with a Si one) has been recently published in the literature [35]. Our calculated stereoselectivity for system IIIa was not particularly encouraging with respect to the analogous system IId being the energetic (free energies) difference between the two TSs, with facial selectivities of 2.5 (2.2) kcal/mol and 3.8 (3.1) kcal/mol, respectively. The smaller CCN angle in complex IId ( Figure 4A,B) forced the i Pr groups on the N-aryl ring closer to the active site, increasing the steric ligand-monomer interactions (3.61 Å) with respect to the Si-bridged system ( Figure 4C,D) (3.88 Å). The preferred configuration of the growing chain was similar for IId and IIIa, and in both cases, we noted the absence of the chiral configuration of the growing chain [41]. The ASM-NEDA analysis ( Table 2) clarified these findings, especially the ∆∆E Strain(Mon) , which represents the principal contribution to the ∆∆E Strain and is higher for system IId (4.7 kcal/mol) compared to system IIIa (3.5 kcal/mol). However, it has been claimed that the suitable modification of siliconbridged pyridylamido-hafnium complexes may effectively reach a higher stereoselectivity, and when we performed DFT calculations on the cyclo-(CH 2 ) 4 Si bridged complex (IIIa) employed by Hagadorn [35], we found that IIIb was more stereoselective than IIIa (Table 1). The presence of a cyclic substituent on the Si-bridge rather than two methyl groups must be regarded as the reason why IIIb produces a more stereoregular iPP than IIIa. As a matter of fact, the -(CH 2 ) 4 -substituent on the bridge makes the complex more constrained, reducing the C-Si-N angle, thereby forcing the N-aryl fragment closer to the monomer ( Figure 5).  In agreement with such statements, the %VBur steric map analysis revealed that there were no notable differences between systems IId and IIIa ( Figure 3D,E), whereas IIIb In agreement with such statements, the %V Bur steric map analysis revealed that there were no notable differences between systems IId and IIIa ( Figure 3D,E), whereas IIIb ( Figure 3F) showed larger %V Bur values in the NW and NE quadrants, in agreement with a higher stereoselectivity. The ASM-NEDA results (Table 2) confirmed that the enhanced stereoselectivity of this complex was due to the larger variation in the ∆E Strain(Mon) between the 1,2 si and 1,2 re insertions, and a quick visualization of the monomer deformation is reported in Figure S5.  In agreement with such statements, the %VBur steric map analysis revealed that there were no notable differences between systems IId and IIIa ( Figure 3D,E), whereas IIIb ( Figure 3F) showed larger %VBur values in the NW and NE quadrants, in agreement with a higher stereoselectivity. The ASM-NEDA results (Table 2) confirmed that the enhanced stereoselectivity of this complex was due to the larger variation in the ΔEStrain(Mon) between the 1,2 si and 1,2 re insertions, and a quick visualization of the monomer deformation is reported in Figure S5.
Interestingly, an even higher isotacticity is predicted for the polymerization promoted by the Dow system IIe (Table 1); the unsymmetrical substitution of R 1 and R 2 on the C bridge increases the ΔΔEStrain(Cat) contribution (with respect to IIa), although with a Interestingly, an even higher isotacticity is predicted for the polymerization promoted by the Dow system IIe (Table 1); the unsymmetrical substitution of R 1 and R 2 on the C bridge increases the ∆∆E Strain(Cat) contribution (with respect to IIa), although with a slight decrease in the ∆∆E Strain(Mon) ( Table 2). The DFT-optimized geometries for the IIe TSs are reported in Figure S6 and the %V Bur steric map is reported in Figure S4C.
As a final step, we focused on the role of the C Aryl bond (Scheme 1) in the pyridylamido framework, replacing the aryl with heteroaryl groups (IVa). The presence of a heteroatom in place of the C Aryl bond avoids the ligand modification in situ and the experimental propene isotacticity promoted by IVa can be explained by the formation of diastereotopic active sites following the Al i Bu 2 H coordination ( Figure S7). Interestingly, site 1 and site 2 select the same propene enantioface and the stereoselectivity is dictated by the "direct ligand-monomer" for site 1 (Figure S7A,B) and the "chiral growing chain orientation" model for site 2 ( Figure S7C,D) [39]. The ASM-NEDA results for IVa, although unraveling the subtle differences for the ∆E Int contribution at each site, are substantially similar to the ones discussed for Ia (Table 2). This demonstrates the relevance of the ∆∆E Strain(Cat) as the main term for the ∆E Strain variation and as the origin of isotactic propagation. The loss of the additional contribution of the ∆∆E Strain(Mon), is, in the end, the main reason for the lower stereoselectivity calculated for IVa with respect to IIa, IIe, IIIa, and IIIb (Table 1), and the way to increase this stereoselectivity is an unsymmetrical substitution with bulky substituents on the bridging methylene atom [37] analogously to system IIe.

Methodology
The DFT calculations were performed by using Gaussian16 programs [42]. B3LYP hybrid functional [43,44] was employed in conjunction with a polarized split-valence basis set (SVP) for H, C, N, Si, O [45] and LANL2DZ basis and pseudopotential for the metal [46]. The stationary points were characterized using vibrational analyses and these analyses were also used to calculate zero-point energies and thermal (enthalpy and entropy) corrections (298.15 K, 1 bar). Improved electronic energies were obtained from single-point calculations using the TZVP basis set for H, C, N, Si, O [47] and the SDD basis set and pseudopotentials [48] for Hf and Zr (an f function with an exponent of 0.5 was added). The dispersion corrections (EmpiricalDispersion=D3 in the Gaussian package) [49] and solvation contribution (PCM model [50], toluene) were evaluated, thus obtaining ∆G (B3/D3/TZVP/PCM) values. With the ASM model proposed by Bickelhaupt [29,30], we partitioned the ∆E Tot into the ∆E Strain and ∆E Int components, where the former was the energy associated with the reactant deformation required to achieve the geometries necessary for a reaction, and the latter was the energy associated with the strength of their reciprocal interactions. Furthermore, the ∆E Strain contribution was additionally expressed as the sum of the strain of the cationic active species bearing the growing polymer chain (simulated by an i Bu group), ∆E Strain(Cat) , and the propene monomer, ∆E Strain(Mon), calculated with respect to the optimized geometries of each species. By using the NEDA [51] approach, we also decomposed the ∆E Int into its terms, which are: the classical electrostatic interaction (ES), polarization interaction (POL), charge transfer (CT), exchange correlation interaction (XC), and deformation (DEF), which represents the energy required to deform the wavefunction of a fragment in the presence of all the other fragments. The ∆E Tot partitioning into its contributions through the ASM-NEDA model is reported in Scheme 2.
partitioned the ΔETot into the ΔEStrain and ΔEInt components, where the former was th ergy associated with the reactant deformation required to achieve the geometries n sary for a reaction, and the latter was the energy associated with the strength of the ciprocal interactions. Furthermore, the ΔEStrain contribution was additionally expresse the sum of the strain of the cationic active species bearing the growing polymer c (simulated by an i Bu group), ΔEStrain(Cat), and the propene monomer, ΔEStrain(Mon), calcu with respect to the optimized geometries of each species. By using the NEDA [51 proach, we also decomposed the ΔEInt into its terms, which are: the classical electros interaction (ES), polarization interaction (POL), charge transfer (CT), exchange correla interaction (XC), and deformation (DEF), which represents the energy required to de the wavefunction of a fragment in the presence of all the other fragments. The ΔETot titioning into its contributions through the ASM-NEDA model is reported in Schem Scheme 2. ΔETot partitioning through ASM-NEDA model. The NBO version 7 software, coupled with Gaussian16 (in conjunction with the TZVP basis set for H, C, N, O, and Si and the SDD basis and pseudopotentials for Hf), was used to perform the NEDA calculations. The steric maps and the percentage of buried volume for each quadrant (%V Bur ) were computed employing a modified version of the SambVca package [27,28] and the whole computational approach has already been tested on the olefin polymerization catalysis [52]. The steric maps for the neutral mono-inserted species (IIa-IIe and IIIa-IIIb) or the neutral catalytic precursors (Ia, Ib and IVa) were created by setting the transition metal as the center of the sphere, whose radius was set to 3.5 Å.

Conclusions
In conclusion, in this work, we analyzed the origin of the stereoselectivity for propene polymerization promoted by pyridylamido-type catalysts. This catalyst class have emerged within the nonmetallocene family because it allows the formation of block-copolymers [53][54][55][56][57] via living and chain shuttling processes [14], and such molecular architectures are not accessible to ansa-metallocenes [58] and heterogeneous ZN systems [59,60]. The mechanism of stereocontrol in olefin polymerization has been proven to be different from the one proposed for ansa-metallocenes [1,33], as well as for octahedral nonmetallocene ligands [33,61]. We used a combined DFT/%V Bur /ASM-NEDA approach for the computational assessment of the steric and electronic contributions to rationalize the ligand structure/polymer microstructure. By using this methodology, we clarified the effect of the metallacycle size, the chemical nature of the bridge linking the pyridine moiety to the N-aryl fragment, the R, R 1 , and R 2 substituent effects, and, finally, the role of aryl and/or heteroaryl groups. It is worth stressing that the DFT calculations were consistent with the experimental data: hindered substituents at the bridge and the ortho-positions on the aniline fragments may increase the stereoselectivity of propene polymerization, as well as moving from a carbonto silicon-bridge. Analogously, the %V Bur steric maps enabled an easy visualization of the ligand steric hindrance, still reproducing the experimental trend. However, a better understanding of the interplay of these steric and electronic contributions was achieved by the ASM-NEDA analysis and its ∆E (Tot) energy decomposition into the ∆E Strain and ∆E Int contributions. The former term is more relevant than the latter for the origin of stereocontrol, and the additional partitioning of the ∆E Strain into the ∆E Strain(Cat) and ∆E Strain(Mon) revealed how subtle ligand modification (see, e.g., the metallacycle size and the asymmetric R 1 and R 2 substitution on X atom, Scheme 1) increases the propene stereoselectivity.